This invention relates generally to the analysis of particle densities in three-dimensional objects. More particularly, this invention relates to a technique for analyzing anisotropic particle scattering in three-dimensional objects.
It is frequently desirable to determine the magnitude of neutrally-charged particle densities, especially nuclear particles, such as neutron, gamma-ray, and X-ray particle densities, in regions where the densities exhibit a significant spatial gradient. Such conditions will exist wherever the particles are xe2x80x9cstreamingxe2x80x9d from regions of high density, such as in or near the particle source, into regions of lower particle density. An accurate determination of the particle concentrations under these conditions has utility for a variety of radiation monitoring and design applications, including the determination of radiation levels and particle irradiation effects in regions outside the active core of nuclear reactors. Particle concentration information is also important for the design and evaluation of radiation shielding and radiation material shipping and handling devices. Particle density information is also critical while evaluating irradiation effects on biological bodies resulting from man-made and natural radiation sources.
In order to accurately determine the magnitude of neutrally-charged particle densities in applications characterized by significant spatial gradients, it is necessary to consider angular variations in particle scattering in order to determine the preferred directions of particle motion. Evaluations that preserve the angular dependence of particle scattering interactions utilize xe2x80x9canisotropic scatteringxe2x80x9d considerations, as opposed to xe2x80x9cisotropic scatteringxe2x80x9d evaluations, wherein particle scattering is assumed to be equally likely in any direction with no preferential directions of particle motion.
Two general approaches may be utilized to characterize the transport of neutrally-charged particles: stochastic methods and deterministic methods. Traditional implementations of each approach have demonstrated disadvantages when applied to the evaluation of particle transport in realistic three-dimensional applications.
Stochastic evaluations, such as Monte Carlo techniques, are based upon an assessment of the probabilistic nature of particle interactions. Arbitrary geometry techniques have been utilized to permit the representation of complex bodies in three-dimensional space. However, stochastic methods suffer from the necessity of tracking an inordinately large number of particle interactions in order to characterize highly anisotropic particle fields, such as those present outside reactor cores, with any reasonable degree of accuracy. Even with the current generation of computing systems, this limitation restricts the practical application of stochastic techniques to applications involving small spatial gradients and, generally, relatively small spatial geometries.
The limitations of stochastic techniques has led to increased reliance upon deterministic methods in the evaluation of particle transport in large geometry systems. The most accurate deterministic methods rely upon simplified formulations of the integro-differential Boltzmann particle transport equation.
A preferred implementation of the Boltzmann equation that achieves accurate results while providing a high degree of flexibility in modeling complex geometries is the integral transport formulation. This formulation is utilized for collision probability methodologies and characteristic solution methodologies that are frequently the basis of current nuclear core evaluation tools. Unfortunately, traditional formulations of the integral transport methodology do not preserve the angular dependence of particle motion, thus limiting the use of integral transport methods to applications that are characterized by little or no anisotropic scattering effects.
Differential formulations of the Boltzmann equation that preserve angular particle scattering effects have been developed as an alternative to the integral transport methods. Unfortunately, differential formulations suffer from being restricted to fairly regular geometric representations and require fine solution meshing if reasonable accuracy is to be maintained.
In view of the foregoing, it would be highly desirable to provide an accurate particle transport evaluation system that is capable of accurate evaluations in large, complex three-dimensional geometries involving significant anisotropic scattering effects.
The method of the invention is a technique for analyzing anisotropic particle scattering. The method includes the step of establishing a three-dimensional geometric representation of an object. A set of rays is then projected through the three-dimensional geometric representation to produce simulated anisotropic particle scattering. An integral particle transport analysis is then executed on the simulated anisotropic particle scattering to produce particle transport data.
The apparatus of the invention is a computer readable memory to direct a computer to function in a specified manner. The apparatus includes a computer aided design system to establish a three-dimensional geometric representation of an object. The computer aided design system includes a line-of-sight analysis feature to project a set of rays through the three-dimensional geometric representation to produce simulated anisotropic particle scattering. A particle transport analysis program executes an integral particle transport analysis on the simulated anisotropic particle scattering to produce particle transport data.
The invention utilizes a unique formulation of the Boltzmann particle transport equation to provide deterministic integral transport methodology that preserves the angular dependence of particle interactions and particle motion. The invention is especially suited for use in determining neutron, gamma, and X-ray radiation field intensities, and particle distributions in nuclear reactor systems, and in the evaluation of irradiation effects on other bodies of irregular shape. Application of the invention""s CAD geometrical modeling system to the deterministic transport methodology results in an integrated solution system that eliminates restrictions imposed by classical mesh-dependent solution methodologies.